Serving all students

Lately, I have been reading a lot of college schedule books.  One interesting idea I found was a college that offered “Intermediate Algebra for STEM” as well as regular intermediate algebra.

However, I saw an overall pattern that is disturbing.

Math programs tend to respond to struggling students by either creating a new course in addition to the old OR by splitting existing courses into 2 or more parts.

Let me clarify the ‘splitting’ — although I did notice a few places with modules (same semester), what I saw more was partial courses to be taken over an entire semester.  Beginning algebra might be a deliberate 2 or 3 semester experience (if all parts are passed); intermediate algebra might be another 2 or 3 semester experience.  The only way this pattern can be justified is by meeting two criteria:

1. A pass rate approaching unity (>90% in every segment)     AND
2. A retention rate approaching unity (>90% continue to the next segment)

These conditions still only allow about 50% of those starting beginning algebra to complete intermediate algebra after a 4-semester sequence (.91^7 = 51.7%).  The more typical 60% pass rate, combined with a more typical 80% retention rate, suggests a whopping 7% of students completing both algebra courses.  Most students are not done with intermediate algebra; getting to pass a college math course would happen for about 3% of those who start a beginning algebra sequence.

The issue here is not whether something needs to be done.  A significant portion (a minority, but non-trivial group) of our students have excessive struggles in spite of good effort on their part in the presence of a good classroom.  My own gut-level estimate is that approximately 20% of students need something more to help them succeed in a traditional algebra course.

Clearly, this is one of the motivations for the New Life courses, Mathematical Literacy and Algebraic Literacy.  These designs provide a more diverse curriculum, with reasoning emphasized, which is meant to help more students succeed.

However, not all institutions are able to implement the Literacy math courses at this time; some institutions will take 5 years to reach that stage.  What should the rest of us do?

I suggest this principle as being a valid guideline for our work with all students (including those who struggle):

The math curriculum should provide a one semester experience at each ‘level’ for all students.

Our current levels are beginning algebra and intermediate algebra.  Courses before beginning algebra have their own issues, and we need to justify their  existence. A beginning algebra course should be one semester, whether a student needs minimal support or maximal support.  A intermediate algebra course should be one semester, whether a student needs minimal support or maximal support.

So, instead of a two-semester beginning algebra sequence, we could offer an expanded class time version of beginning algebra.  If we think students need twice as much ‘instruction’, then we could offer a 8-class-hour per week version of a 4-credit course; at many institutions, this translates into a 4 credit course with 8 billing hours.

Most of us introduce the sequence of partial courses in response to lower pass rates for a group of struggling students.  My college did this for about 10 years.  Our rationale was that only 25% to 30% of the struggling group passed the single course, compared to 60% for the remainder of the students.  However, our best efforts only achieved 60% pass rate in the two half-courses; this resulted in about 29% of the students completing both halves — about the same rate as completed the single course.

Helping struggling students is not about providing more courses in a sequence.  Helping struggling students is much more about what we do in one course, in one semester.  Whether ‘struggling’ comes from learning disabilities (the most common reason), or historical accidents of the student (no diploma, no GED), helping students should not hurt students chances of completion.  In the political parlance, we are talking about societies most vulnerable adults.  Our work should be about catching them up, not setting them further behind.

Let’s drop those sequences of partial courses.  The design can not succeed as a strategy.  Let’s create some truly helpful solutions that fit within one semester.

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1 Comment

• 

  By schremmer, November 19, 2013 @ 4:45 pm

  Taking the course content of “beginning algebra”and “intermediate algebra” as given leaves no alternative but to slice them this way or that way.

  On the other hand:

  “Taking course content as given …] has produced valuable insights and useful results. However, it ignores the possibility of improving pedagogy by reconstructing course content.”

  Adapted from a passage in Hestenes’ Oersted Medal Lecture 2002.

  Regards
  –schremmer

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